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This approach involves counting the number of ones and zeros in each row and each column beforehand. Then, for each element in the grid, compute the corresponding value in the difference matrix using the precomputed counts.
Time Complexity: O(m * n) where m is the number of rows and n is the number of columns. This involves going through each element of the grid twice; once for counting and once for filling the difference matrix.
Space Complexity: O(m + n) for storing counts of ones and zeros for each row and column.
1using System;
2
3public class Solution {
4 public int[][] DifferenceMatrix(int[][] grid) {
5 int m = grid.Length;
6 int n = grid[0].Length;
7 int[] onesRow = new int[m];
8 int[] zerosRow = new int[m];
9 int[] onesCol = new int[n];
10 int[] zerosCol = new int[n];
11
12 // Precompute the number of ones and zeros in each row and column
13 for (int i = 0; i < m; i++) {
14 for (int j = 0; j < n; j++) {
15 if (grid[i][j] == 1) {
16 onesRow[i]++;
17 onesCol[j]++;
18 } else {
19 zerosRow[i]++;
20 zerosCol[j]++;
21 }
22 }
23 }
24
25 int[][] diff = new int[m][];
26 // Create the difference matrix
27 for (int i = 0; i < m; i++) {
28 diff[i] = new int[n];
29 for (int j = 0; j < n; j++) {
30 diff[i][j] = onesRow[i] + onesCol[j] - zerosRow[i] - zerosCol[j];
31 }
32 }
33 return diff;
34 }
35}
36The C# code follows the same logical steps as other implementations. Arrays are employed for precomputing the counts of ones and zeros, which are then used to derive the elements of the result difference matrix efficiently.
This approach seeks to optimize the space complexity by calculating necessary counts and the result matrix in a single pass, thereby avoiding separate storage for ones and zeros counts.
Time Complexity: O(m * n) because every element is iterated over during the counting and result generation stages.
Space Complexity: O(n) due to the storage of column ones, improving from O(m + n).
This JavaScript code optimizes calculation by keeping count computations in separate sections, using reduce for summing row ones, resulting in a less memory-taxing solution while retaining precision and promptness of result construction.